The fundamental difference between grading GRE essays and reviewing scientific papers submitted for publication has been has been cogently discussed in several previous answers. The fundamental difference between reviewing grant applications and papers for publication has not.
Publications. When a paper is submitted to a journal it is usually supposed to be a finished product, or at least one finished step toward a defined goal. It is truly difficult
to find reviewers who are able to assess the importance of a paper and to
find every gap in reasoning or every imperfection in technique, but at least
reviewers of journal articles have the results of a piece of research at hand.
A potential Nobel paper may cover material so new or so far off the beaten track that it will be especially difficult to review fairly. A paper resubmitted after several years may have been based on procedures or techniques that have
been considerably refined in the meantime. So maybe they were state
of the art at the time of original submission, but are now 'seriously flawed' in terms of currently
available methods. So it is hardly surprising that reviewers don't score 100% on
However, even though reviewers are unpaid, overworked volunteers, working with no specialized training or feedback on the details of reviewing, I think it is surprising how well journal reviewing works in practice.
Grants. By contrast, making judgments about research grants is an entirely different
kind of activity. Some years ago (when US federal funding was available at a much higher level than it is now), I spent several years at a federal agency with a reasonably large budget for supporting basic and applied research in a variety of scientific fields. So I will try to address this part of the picture briefly. I will begin by saying that I am not at all surprised that a panel of research scientists would find the funding of NIH (or any other US government agency) to
be 'no better than a lottery'.
Generally speaking, if you know exactly what you are doing,
how long it will take, and how much it will cost, you're not doing research. Reviewers can often be useful, in assessing a proposer's track record of success and providing a rough idea whether the proposer is competent to
undertake research in a particular area. (I should add that most program directors are well aware of the standards, biases, foibles, and strengths of the reviewers they use. I was seldom surprised by the contents of a requested review, but the few surprises were extremely valuable.) However, reviewer input is only a part of the picture.
Going beyond reviewer input, program directors in granting agencies have to take other factors into account. To some degree they must consider
financial, political, and infrastructural factors. 'Political' usually means that that money was appropriated or donated
specifically to support a particular scientific goal. Infrastructural concerns
may center on developing technologies that are agency goals, training graduate students in fields where there are not enough researchers, whether the institution requesting the grant has the sophistication for adequate stewardship, and so on.
US, agencies such as NIH, NSF, DoE, EPA, various defense agencies, and various privately funded foundations may have very different goals. However clearly these agency
missions and objectives may be spelled out in 'requests for proposals', they are often ignored by grant applicants, who might make a better case for their work if the
appropriate connections were made clear.
In spite of these constraints on awarding of grants, program directors strive to
support nothing but the highest quality science, and I believe they usually succeed at that. In my experience, almost all of them view themselves as scientists first and agency bureaucrats second.
Often their success is with the considerable help of reviewers, but sometimes not.